Theme Essential Question: How can you use numerical and algebraic expressions, equations, and inequalities to solve real-life mathematical problems?
Essential Questions: How are algebraic expression written, interpreted, simplified, and evaluated?
Standards:
7. EE.1 Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Objectives:
The student will define, apply, and use algebraic vocabulary.
The student will translate verbal statements to algebraic expressions and algebraic expression to verbal statements.
The student will evaluate algebraic expressions.
The student will write equivalent algebraic statement by combining like terms and/or using the distributive property.
The student will model a factorable algebraic expression.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team: Mathematical Practice #8, look for and express regularity in repeated reasoning, would be appropriate with combining like terms and the distributive property. During this unit, students will be writing expressions and equations, check answers for reasonability, and looking for shortcuts as they simplify expressions. After this lesson, seven of the eight Mathematical Practices, should be part of the student’s approach to learning and expression mathematics.
Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022 Students continue to use properties that were initially used with whole numbers and now develop the understanding that properties hold for integers, rational and real numbers.
Provide opportunities to build upon this experience of writing expressions using variables to represent situations and use the properties of operations to generate equivalent expressions. These expressions may look different and use different numbers, but the values of the expressions are the same.
One method that students can use to become convinced that expressions are equivalent is by substituting a numerical value for the variable and evaluating the expression.
For example: Is 5(3 + 2x) equal to 53 + 52x? Let x = 6 and substitute 6 for x in both equations. 5(3 + 26) = 53 + 526 5(3 + 12) = 15 + 60 5(15) = 75 75 = 75
Provide opportunities for students to use and understand the properties of operations. These include: the commutative, associative, identity, and inverse properties of addition and of multiplication, and the zero property of multiplication. Another method students can use to become convinced that expressions are equivalent is to justify each step in the simplification process with an operation property.
The students will design and write eight algebraic statement (example: twice the sum of 4 and x) on the outside triangles and the corresponding algebraic expressions (example: 2(4 + x)) on the inside triangles.
The students will design and write eight algebraic expressions that can be simplified by combine like terms and/or distributive property (example: 2(x + 3) -1)) and the corresponding simplified expressions (example: 2x + 5) on the inside triangles.
Allow children time to play with each other. (Sample instruction for playing is located, Teaching the Common core Math Standards with Hands-On Activities, p. 21)
Key Questions
What words can be used to indicate addition, subtraction, multiplication and division?
What are some key words or phrases that denote the usage of parenthesis?
How do you define, explain, and use the algebraic phrase like terms?
How do you use the commutative, associative, and distributive property to simplify expressions?
Observable Student Behaviors
The student can convert word phrases to algebraic expressions and vise versa.
The student can simplify or expand an algebraic expression using like terms and/or the distributive properties.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Numerical expressions Algebraic expressions Constant Variables Coefficient Term Like terms Combining like terms Factors Common factor Factoring expressions Simplified expressions Distributive properties Commutative properties Associative properties Identity properties Equivalent Degree Leading coefficient Base Exponent
Suggested Activities:
Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 3-1, p. 59-62
ABC Mastering the Common Core in Mathematics
Vocabulary Chapter 8-1, p. 89
Evaluate an Expression Chapter 8-2, p. 90
Translation of Expressions Chapter 8-3, p. 91-94
Combining Like Terms Chapter 9-3, p. 102
Distributive Property Chapter 9.4, p.102-103
Teaching the Common Core Math Standards with Hands-On Activities,
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM 8th, GP 2, p. 1-28
Glencoe 7th Grade PreAlgebra, Chapter 1-3, p. 17-21
Lesson Plan in Word Format (Click Cancel if asked to Log In)
Resources:
Professional Texts:
Literary Texts
Mathematics in Children's Literature:
Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.
Related Topics: addition, arithmetic, assessment, division, integers, multiplication, negative number, positive number, positive part of the operand, subtraction, whole numbers
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html This Algebraic Expressions Millionaire Game can be played online alone or in two teams. For each question you have to identify the correct mathematical expression that models a given word expression. You could also use it as classroom challenge and have students write their answers on white board and check.
Content: Algebraic Expressions
Theme Essential Question:
How can you use numerical and algebraic expressions, equations, and inequalities to solve real-life mathematical problems?
Essential Questions:
How are algebraic expression written, interpreted, simplified, and evaluated?
Standards:
Objectives:
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team:
Mathematical Practice #8, look for and express regularity in repeated reasoning, would be appropriate with combining like terms and the distributive property. During this unit, students will be writing expressions and equations, check answers for reasonability, and looking for shortcuts as they simplify expressions. After this lesson, seven of the eight Mathematical Practices, should be part of the student’s approach to learning and expression mathematics.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022
Students continue to use properties that were initially used with whole numbers and now develop the understanding that properties hold for integers, rational and real numbers.
Provide opportunities to build upon this experience of writing expressions using variables to represent situations and use the properties of operations to generate equivalent expressions. These expressions may look different and use different numbers, but the values of the expressions are the same.
One method that students can use to become convinced that expressions are equivalent is by substituting a numerical value for the variable and evaluating the expression.
For example: Is 5(3 + 2x) equal to 53 + 52x?
Let x = 6 and substitute 6 for x in both equations.
5(3 + 26) = 53 + 526
5(3 + 12) = 15 + 60
5(15) = 75
75 = 75
Provide opportunities for students to use and understand the properties of operations. These include: the commutative, associative, identity, and inverse properties of addition and of multiplication, and the zero property of multiplication. Another method students can use to become convinced that expressions are equivalent is to justify each step in the simplification process with an operation property.
Assessment:
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Like terms Combining like terms Factors Common factor Factoring expressions Simplified expressions Distributive properties Commutative properties Associative properties Identity properties Equivalent Degree Leading coefficient Base Exponent
Suggested Activities:
Gizmo Lessons – None Available at this time
Highly Recommended
http://illustrativemathematics.org/illustrations/643 (7.EE.1)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Diverse Learners
Homework: (Teacher Discretion)
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Lesson Plan in Word Format (Click Cancel if asked to Log In)
Resources:
Professional Texts:
Literary Texts
Informational Texts
Art, Music, and Media
Manipulatives
Games
- http://www.mathchimp.com/7thGrade.php
- http://www.sumdog.com/ A variety of games covering many math topics
- http://www.mathplayground.com/SMP_index.html
- Connect Four game format:
Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.Videos
- Discovery Learning http://www.discoveryeducation.com/
- The Teaching Channel
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.Smartboard Lesson, Promethean Lessons
- ALGEBRAIC EXPRESSIONS MILLIONAIRE
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.htmlThis Algebraic Expressions Millionaire Game can be played online alone or in two teams. For each question you have to identify the correct mathematical expression that models a given word expression. You could also use it as classroom challenge and have students write their answers on white board and check.
Other Activities, etc.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6